Achieving 'realism' in a CGI image is not easy, but it all boils down to attention to detail. We all have pretty good built-in bulls&%t detectors and can tell when something doesn't look quite right, but in some cases it can be difficult to know exactly why. There are a bunch of elements that all need to be considered when attempting to create a realistic-looking render:
1) The model: Using Rudy's excellent examples above, the 'Knobs' image in particular, notice the tiny gap between the knobs and the font panel, the rounding of the edges of the front panel as they meet the case, the gap in the case suggesting it's made of two halves. In the MorseKey image, notice how the shiny metal armature is a bit convex on top, just as would happen when polishing a piece of metal like that. Notice how its edges are not perfectly sharp, which is easy to achieve in the digital world but much harder (and more dangerous!) in reality. This sort of attention to the reality of engineering is important and when it is overlooked the image can look too 'perfect', a sure sign that it's not real.
2) Materials: While Anim8or's materials are relatively simple compared to other 3D packages they are still complex with a massive range of possibilities. Getting to grips with the ART parameters is critical, it has its own set of instructions and permits things like complex reflections, glossy surfaces, dielectrics, refractions etc. What makes glass look like glass, considering it's effectively transparent? Again, using Rudy's Vase6 render above, it's the complex interplay between transparency, dielectics, refraction and reflection that makes it look so real. The best advice I can give is to learn what the material settings do, reconstruct the samples in the literature, and do a bunch of test renders to see what's going on. There's really no trick to this, it just takes time.
3) Lighting: As has been said before, lighting is one of the most critical things to get right. For example, consider a render of a comms satellite in Earth orbit. Technically there will only be a single light source (the Sun) but it will also be illuminating the Earth below, which will be acting as a second, diffuse, bluish light source from 'below'. Parts of the satellite hidden from both the Sun and Earth will be totally black with nothing to illuminate them (other than starlight I guess). However, a scene in a room lit by sunlight streaming through an open window will be very different, as the sunlight will be bouncing around the room banishing most shadows and casting different shades of light on the objects. This 'secondary' illumination can be simulated in a rudimentary way with the ambient light setting and some more complex systems can simulate secondary (tertiary etc.) lighting, but well-considered positioning of fill lights in an Anim8or scene can go a long way towards improving the realism of a scene. Having an understanding of how light behaves in different situations is critical in the accurate positioning of these fill lights.
4) Filth: As I said above, perfection is a sure sign that something's off. Looking at Rudy's MorseKey image, imagine if there were fingerprints on the shiny metal part and the Bakelite knob or a bit of rust pitting; if this was the case I'm not sure I would have recognised it as anything other than a photograph of a real object. Imperfection is everywhere, from the rough and damaged edges of a desktop to rain spots on a window pane or machining marks on a polished metal surface. Simulating imperfection can go a long way towards achieving realism, mostly it will be done in the materials but thinking about it at the modelling stage is also worthwhile.
There are other things that can destroy the perception of reality, such as movement in an animation that doesn't respect physics, but I would say these are the main ones. I don't believe there are 'tricks' to achieving realism, every realistic CGI image I have ever seen (here or elsewhere) has been created by someone with lots of experience and folders full of earlier renders, many of which they would be embarrassed to share now. It's a learning curve, every render you do will be better than the one before it. The best advice I can give is build, render, post in forums like this one and take on board what others say.